Which of the following are sets? Justify your answer.

The collection of all short boys of your class.

What do you mean by a binary relation on a set A? Define the domain and range of relation on A.

Match each of the sets on the left described in the roster from with the same set on the right described in the set-builder from:

List all the elements of each of the sets given below.

H = {x : x ϵ Z, |x| ≤ 2}.

Rewrite the following statements using the set notation:

(i) a is an element of set A.

(ii) b is not an element of A.

(iii) A is an empty set and B is a nonempty set.

(iv) A number of elements in A is 6.

(v) 0 is a whole number but not a natural number.

If A = {1, 2}, find A × A × A.

Find a and b when (a – 2b, 13) = (7, 2a – 3b)

Mark the correct alternative in the following:

Let F₄ be the set of all parallelograms, F₂ the set of all rectangles, F₃ the set of all rhombuses, F₄ the set of all squares and F₅ the set of trapeziums in a plane. Then F₁ may be equal to

Let R be set of points inside a rectangle of sides a and b (a, b > 1) with two sides along the positive direction of x-axis and y-axis. Then

Write the following sets in roster from:

J = {x : ϵ R and x² + x – 12 = 0}.

List all the elements of each of the sets given below.

D = {x : x = n², n ϵ N and 2 ≤ n ≤ 5}.